Which Axiom from the H-A Axioms is used to prove the following tautology? (A → ¬A) → ((A → A) → (A → ¬A) 1 3 4 2.

Q: Construct direct proofs to show that the following symbolic arguments are valid.  Commas mark the…

A: The proof is given in step 2

Q: Use propositional logic to prove that the following argument is valid.

A: Introduction: When identical statement variables are used to denote the component statements, two…

Q: Compare the following compound statements. (pVq) ∧  ~q                ;             pV (~q ∧ ~p)…

A: A compound statement is a tautology if its truth value is always T, regardless of the truth values…

Q: Simplify the following statement: [(p→q) ∨ (q →r)] ∧ (r→s) (a) Using a truth table, show that p∨…

A: In the given question we have to simplify the given statement s.t  we will simplify it directly…

Q: Use the laws of propositional logic to prove that the following compound propositions are…

A: To use law of propositional logic to prove that the below compound propositions are tautologies.…

Q: (p V q) V (q → p) is a

A:

Q: (P → (Q v R))  –| |–  (P → Q) v (P → R) PHIL 2303 Logic. 8.5. Tautologies and Equivalences.…

A: We use the following identity in the proof in both ways.       X → Y ≡ ~X v Y    [ ~ denotes…

Q: 1. Use propositional logic (direct or indirect proof) to prove the following theorems: a. - (p v ¬q)…

A:

Q: Prove that (P => Q) ↔ (¬P V Q) is a tautology.

A: We have to prove that  is a tautology.